Question

1. Use MATLAB to implement the Fixed Increment Perceptron Learning Algorithm described below: Given m input patterns X1, X2, ..., Xm each input pattern Xj = (x1, x2, ..., xn) and Given m corresponding target outputs y1, y2, ..., ym Step 1: Create a perceptron with n + 1 input neurons x0, x1, ..., xn where x0 = 1 is the bias input. Let y be the output neuron Step 2: Initialize w = (w0, w1, ..., wn) to random weights Step 3: Iterate through the input patterns Xj, j = 1, 2, ..., m to adjust the weights: Step 3.1: Compute the output using the current weights y = phi(sum_{i=0}^n w_i x_i) Step 3.2: If the input pattern was not classified correctly, i.e. if y != y_j, adjust the weights using the perceptron learning rule. w'_i = w_i + a e x_i Otherwise, leave the weights unchanged. Step 3.3: If all patterns have been classified correctly, output the weights and exit. Otherwise, repeat step 3 once more. 2. The following is a training set for a 2-classification problem. Apply the Fixed Increment Perceptron Learning Algorithm of Problem 1 to the training set and obtain the weights. Take alpha = 0.01 Inputs | Class x1 | x2 | y 0.25 | 0.353 | 0 0.25 | 0.471 | 1 0.5 | 0.353 | 0 0.5 | 0.647 | 1 0.75 | 0.705 | 0 0.75 | 0.882 | 1 1 | 0.705 | 0 1 | 1 | 1 3. Let alpha take the values 0.01, 0.05, 0.1, 0.5, 1, 2 or 5, and repeat the program for Problem 2 for each value of alpha and count the number of training epochs required. How does the value of alpha affect the training process? 4. Modify the stopping condition by replacing Step 3.3 of the Fixed Increment Perceptron Learning Algorithm to exit when the Euclidian distance between the weight before and after the training epoch is less than a certain value, 0.001 for instance.

          1. Use MATLAB to implement the Fixed Increment Perceptron Learning Algorithm described below:
Given m input patterns X1, X2, ..., Xm each input pattern Xj = (x1, x2, ..., xn) and
Given m corresponding target outputs y1, y2, ..., ym
Step 1: Create a perceptron with n + 1 input neurons x0, x1, ..., xn where x0 = 1 is the
bias input. Let y be the output neuron
Step 2: Initialize w = (w0, w1, ..., wn) to random weights
Step 3: Iterate through the input patterns Xj, j = 1, 2, ..., m to adjust the weights:
Step 3.1: Compute the output using the current weights y = phi(sum_{i=0}^n w_i x_i)
Step 3.2: If the input pattern was not classified correctly, i.e. if y != y_j, adjust
the weights using the perceptron learning rule.
w'_i = w_i + a e x_i
Otherwise, leave the weights unchanged.
Step 3.3: If all patterns have been classified correctly, output the weights and
exit. Otherwise, repeat step 3 once more.
2. The following is a training set for a 2-classification problem. Apply the Fixed
Increment Perceptron Learning Algorithm of Problem 1 to the training set and obtain
the weights. Take alpha = 0.01
Inputs | Class
x1 | x2 | y
0.25 | 0.353 | 0
0.25 | 0.471 | 1
0.5 | 0.353 | 0
0.5 | 0.647 | 1
0.75 | 0.705 | 0
0.75 | 0.882 | 1
1 | 0.705 | 0
1 | 1 | 1
3. Let alpha take the values 0.01, 0.05, 0.1, 0.5, 1, 2 or 5, and repeat the program for Problem
2 for each value of alpha and count the number of training epochs required. How does the
value of alpha affect the training process?
4. Modify the stopping condition by replacing Step 3.3 of the Fixed Increment Perceptron
Learning Algorithm to exit when the Euclidian distance between the weight before and
after the training epoch is less than a certain value, 0.001 for instance.

1. Use MATLAB to implement the Fixed Increment Perceptron Learning Algorithm described below:
Given m input patterns X1, X2, ..., Xm each input pattern Xj = (x1, x2, ..., xn) and
Given m corresponding target outputs y1, y2, ..., ym
Step 1: Create a perceptron with n + 1 input neurons x0, x1, ..., xn where x0 = 1 is the
bias input. Let y be the output neuron
Step 2: Initialize w = (w0, w1, ..., wn) to random weights
Step 3: Iterate through the input patterns Xj, j = 1, 2, ..., m to adjust the weights:
Step 3.1: Compute the output using the current weights y = phi(sumi=0^n wi xi)
Step 3.2: If the input pattern was not classified correctly, i.e. if y != yj, adjust
the weights using the perceptron learning rule.
w'i = wi + a e xi
Otherwise, leave the weights unchanged.
Step 3.3: If all patterns have been classified correctly, output the weights and
exit. Otherwise, repeat step 3 once more.
2. The following is a training set for a 2-classification problem. Apply the Fixed
Increment Perceptron Learning Algorithm of Problem 1 to the training set and obtain
the weights. Take alpha = 0.01
Inputs | Class
x1 | x2 | y
0.25 | 0.353 | 0
0.25 | 0.471 | 1
0.5 | 0.353 | 0
0.5 | 0.647 | 1
0.75 | 0.705 | 0
0.75 | 0.882 | 1
1 | 0.705 | 0
1 | 1 | 1
3. Let alpha take the values 0.01, 0.05, 0.1, 0.5, 1, 2 or 5, and repeat the program for Problem
2 for each value of alpha and count the number of training epochs required. How does the
value of alpha affect the training process?
4. Modify the stopping condition by replacing Step 3.3 of the Fixed Increment Perceptron
Learning Algorithm to exit when the Euclidian distance between the weight before and
after the training epoch is less than a certain value, 0.001 for instance.

Added by Jose Miguel W.

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